In this paper we consider Z-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z-actions of expansive rank one). If α is such a Z-action on an infinite compact connected abelian group X, then every expansive element α of this action has a dense group ∆αn(X) of homoclinic points. For different ...

We construct an infinite family of representations of finite groups with an irreducible adjoint action and we give an application to the question of lacunary of Frobenius traces in Galois representations. 2010 Mathematics Subject Classification. 11F80, 11R45, 20C15.

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

For a Lie groupoid G over smooth manifold M we construct the adjoint action of étale # germs local bisections on algebroid g . With this action, form associated convolution C c ∞ ( ) / R -bialgebra , We represent in algebra transversal distributions This construction extends Cartier-Gabriel decomposition Hopf with finite support group.

Including tracer data into geostatistically based methods of inverse modeling is computationally very costly when all concentration measurements are used and the sensitivities of many observations are calculated by the direct di€erentiation approach. Harvey and Gorelick (Water Resour Res 1995;31(7):1615±26) have suggested the use of the ®rst temporal moment instead of the complete concentration...

1 2 supersymmetric gauge theory coupled to chiral matter in the adjoint representation, and investigate the one-loop 1 2 supersymmetric theories (i.e. theories defined on non-anticommutative super-space) have recently attracted much attention[1]–[4]. Such theories are non-hermitian and only have half the supersymmetry of the corresponding N = 1 theory. These theories are not power-counting reno...

In this short note, we construct a right adjoint to the functor which associates ring R equipped with group action its twisted ring. This admits an interpretation as semilinearization, in that it sends R-module of semilinear automorphisms module. As immediate corollary, provide novel proof classical observation modules over are base together action.

The observable algebra O of SOq(3)-symmetric quantum mechanics is generated by the coordinates Pi and Xi of momentum and position spaces (which are both isomorphic to the SOq(3)-covariant real quantum space IR 3 q). Their interrelations are determined with the quantum group covariant differential calculus. For a quantum mechanical representation of O on a Hilbert space essential self-adjointnes...

The three-dimensional quantum Euclidean space is an example of a non-commutative space that is obtained from Euclidean space by q-deformation. Simultaneously, angular momentum is deformed to soq(3), it acts on the q-Euclidean space that becomes a soq(3)-module algebra this way. In this paper it is shown, that this algebra can be realized by differential operators acting on C∞ functions on R. On...

In recent work ([9],[10]), Kostant and Wallach construct an action of a simply connected Lie group A ≃ C( n 2 ) on gl(n) using a completely integrable system derived from the Poisson analogue of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In [9], the authors show that A-orbits of dimension ( n 2 ) form Lagrangian submanifolds of regular adjoint orbits in gl(n). They describe the o...